From concept of reflection of function, function Option(C) g(x) = [tex]-x^{2} - 3[/tex].
What is reflection of function ?
Reflection of function is defined as the mirror image of the given function with respect to any defined axis, shifted at a constant interval of coordinate. The function obtained from the reflection has the same shape and curve but of different orientation.
How to obtain the function from the given reflection ?
The original function is f(x) = [tex]x^{2}[/tex]
g(x) is the reflection of the function f(x) which is being shifted to the interval of 3 with respect to the negative x-axis.
Thus, to obtain the function g(x), the original function f(x) = [tex]x^{2}[/tex] is being changed to - [tex]x^{2}[/tex] and also the coordinate is 3 units negative of x-axis.
Thus, g(x) = [tex]-x^{2} - 3[/tex].
Therefore, from concept of reflection of function, function Option(C) g(x) = [tex]-x^{2} - 3[/tex].
To learn more about reflection of function, refer -
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